module Network.HTTP.MD5Aux (md5, md5s, md5i, MD5(..), ABCD(..), Zord64, Str(..), BoolList(..), WordList(..)) where import Data.Char (ord, chr) import Data.Bits (rotateL, shiftL, shiftR, (.&.), (.|.), xor, complement) import Data.Word (Word32, Word64) rotL :: Word32 -> Int -> Word32 rotL x = rotateL x type Zord64 = Word64 -- ===================== TYPES AND CLASS DEFINTIONS ======================== type XYZ = (Word32, Word32, Word32) type Rotation = Int newtype ABCD = ABCD (Word32, Word32, Word32, Word32) deriving (Eq, Show) newtype Str = Str String newtype BoolList = BoolList [Bool] newtype WordList = WordList ([Word32], Word64) -- Anything we want to work out the MD5 of must be an instance of class MD5 class MD5 a where get_next :: a -> ([Word32], Int, a) -- get the next blocks worth -- \ \ \------ the rest of the input -- \ \--------- the number of bits returned -- \--------------- the bits returned in 32bit words len_pad :: Word64 -> a -> a -- append the padding and length finished :: a -> Bool -- Have we run out of input yet? -- Mainly exists because it's fairly easy to do MD5s on input where the -- length is not a multiple of 8 instance MD5 BoolList where get_next (BoolList s) = (bools_to_word32s ys, length ys, BoolList zs) where (ys, zs) = splitAt 512 s len_pad l (BoolList bs) = BoolList (bs ++ [True] ++ replicate (fromIntegral $ (447 - l) .&. 511) False ++ [l .&. (shiftL 1 x) > 0 | x <- (mangle [0..63])] ) where mangle [] = [] mangle xs = reverse ys ++ mangle zs where (ys, zs) = splitAt 8 xs finished (BoolList s) = s == [] -- The string instance is fairly straightforward instance MD5 Str where get_next (Str s) = (string_to_word32s ys, 8 * length ys, Str zs) where (ys, zs) = splitAt 64 s len_pad c64 (Str s) = Str (s ++ padding ++ l) where padding = '\128':replicate (fromIntegral zeros) '\000' zeros = shiftR ((440 - c64) .&. 511) 3 l = length_to_chars 8 c64 finished (Str s) = s == "" -- YA instance that is believed will be useful instance MD5 WordList where get_next (WordList (ws, l)) = (xs, fromIntegral taken, WordList (ys, l - taken)) where (xs, ys) = splitAt 16 ws taken = if l > 511 then 512 else l .&. 511 len_pad c64 (WordList (ws, l)) = WordList (beginning ++ nextish ++ blanks ++ size, newlen) where beginning = if length ws > 0 then start ++ lastone' else [] start = init ws lastone = last ws offset = c64 .&. 31 lastone' = [if offset > 0 then lastone + theone else lastone] theone = shiftL (shiftR 128 (fromIntegral $ offset .&. 7)) (fromIntegral $ offset .&. (31 - 7)) nextish = if offset == 0 then [128] else [] c64' = c64 + (32 - offset) num_blanks = (fromIntegral $ shiftR ((448 - c64') .&. 511) 5) blanks = replicate num_blanks 0 lowsize = fromIntegral $ c64 .&. (shiftL 1 32 - 1) topsize = fromIntegral $ shiftR c64 32 size = [lowsize, topsize] newlen = l .&. (complement 511) + if c64 .&. 511 >= 448 then 1024 else 512 finished (WordList (_, z)) = z == 0 instance Num ABCD where ABCD (a1, b1, c1, d1) + ABCD (a2, b2, c2, d2) = ABCD (a1 + a2, b1 + b2, c1 + c2, d1 + d2) (*) = error "(*){ABCD}: no instance method defined" signum = error "signum{ABCD}: no instance method defined" fromInteger = error "fromInteger{ABCD}: no instance method defined" abs = error "abs{ABCD}: no instance method defined" -- ===================== EXPORTED FUNCTIONS ======================== -- The simplest function, gives you the MD5 of a string as 4-tuple of -- 32bit words. md5 :: (MD5 a) => a -> ABCD md5 m = md5_main False 0 magic_numbers m -- Returns a hex number ala the md5sum program md5s :: (MD5 a) => a -> String md5s = abcd_to_string . md5 -- Returns an integer equivalent to the above hex number md5i :: (MD5 a) => a -> Integer md5i = abcd_to_integer . md5 -- ===================== THE CORE ALGORITHM ======================== -- Decides what to do. The first argument indicates if padding has been -- added. The second is the length mod 2^64 so far. Then we have the -- starting state, the rest of the string and the final state. md5_main :: (MD5 a) => Bool -- Have we added padding yet? -> Word64 -- The length so far mod 2^64 -> ABCD -- The initial state -> a -- The non-processed portion of the message -> ABCD -- The resulting state md5_main padded ilen abcd m = if finished m && padded then abcd else md5_main padded' (ilen + 512) (abcd + abcd') m'' where (m16, l, m') = get_next m len' = ilen + fromIntegral l ((m16', _, m''), padded') = if not padded && l < 512 then (get_next $ len_pad len' m, True) else ((m16, l, m'), padded) abcd' = md5_do_block abcd m16' -- md5_do_block processes a 512 bit block by calling md5_round 4 times to -- apply each round with the correct constants and permutations of the -- block md5_do_block :: ABCD -- Initial state -> [Word32] -- The block to be processed - 16 32bit words -> ABCD -- Resulting state md5_do_block abcd0 w = abcd4 where (r1, r2, r3, r4) = rounds {- map (\x -> w !! x) [1,6,11,0,5,10,15,4,9,14,3,8,13,2,7,12] -- [(5 * x + 1) `mod` 16 | x <- [0..15]] map (\x -> w !! x) [5,8,11,14,1,4,7,10,13,0,3,6,9,12,15,2] -- [(3 * x + 5) `mod` 16 | x <- [0..15]] map (\x -> w !! x) [0,7,14,5,12,3,10,1,8,15,6,13,4,11,2,9] -- [(7 * x) `mod` 16 | x <- [0..15]] -} perm5 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15] = [c1,c6,c11,c0,c5,c10,c15,c4,c9,c14,c3,c8,c13,c2,c7,c12] perm5 _ = error "broke at perm5" perm3 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15] = [c5,c8,c11,c14,c1,c4,c7,c10,c13,c0,c3,c6,c9,c12,c15,c2] perm3 _ = error "broke at perm3" perm7 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15] = [c0,c7,c14,c5,c12,c3,c10,c1,c8,c15,c6,c13,c4,c11,c2,c9] perm7 _ = error "broke at perm7" abcd1 = md5_round md5_f abcd0 w r1 abcd2 = md5_round md5_g abcd1 (perm5 w) r2 abcd3 = md5_round md5_h abcd2 (perm3 w) r3 abcd4 = md5_round md5_i abcd3 (perm7 w) r4 -- md5_round does one of the rounds. It takes an auxiliary function and foldls -- (md5_inner_function f) to repeatedly apply it to the initial state with the -- correct constants md5_round :: (XYZ -> Word32) -- Auxiliary function (F, G, H or I -- for those of you with a copy of -- the prayer book^W^WRFC) -> ABCD -- Initial state -> [Word32] -- The 16 32bit words of input -> [(Rotation, Word32)] -- The list of 16 rotations and -- additive constants -> ABCD -- Resulting state md5_round f abcd s ns = foldl (md5_inner_function f) abcd ns' where ns' = zipWith (\x (y, z) -> (y, x + z)) s ns -- Apply one of the functions md5_[fghi] and put the new ABCD together md5_inner_function :: (XYZ -> Word32) -- Auxiliary function -> ABCD -- Initial state -> (Rotation, Word32) -- The rotation and additive -- constant (X[i] + T[j]) -> ABCD -- Resulting state md5_inner_function f (ABCD (a, b, c, d)) (s, ki) = ABCD (d, a', b, c) where mid_a = a + f(b,c,d) + ki rot_a = rotL mid_a s a' = b + rot_a -- The 4 auxiliary functions md5_f :: XYZ -> Word32 md5_f (x, y, z) = z `xor` (x .&. (y `xor` z)) {- optimised version of: (x .&. y) .|. ((complement x) .&. z) -} md5_g :: XYZ -> Word32 md5_g (x, y, z) = md5_f (z, x, y) {- was: (x .&. z) .|. (y .&. (complement z)) -} md5_h :: XYZ -> Word32 md5_h (x, y, z) = x `xor` y `xor` z md5_i :: XYZ -> Word32 md5_i (x, y, z) = y `xor` (x .|. (complement z)) -- The magic numbers from the RFC. magic_numbers :: ABCD magic_numbers = ABCD (0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476) -- The 4 lists of (rotation, additive constant) tuples, one for each round rounds :: ([(Rotation, Word32)], [(Rotation, Word32)], [(Rotation, Word32)], [(Rotation, Word32)]) rounds = (r1, r2, r3, r4) where r1 = [(s11, 0xd76aa478), (s12, 0xe8c7b756), (s13, 0x242070db), (s14, 0xc1bdceee), (s11, 0xf57c0faf), (s12, 0x4787c62a), (s13, 0xa8304613), (s14, 0xfd469501), (s11, 0x698098d8), (s12, 0x8b44f7af), (s13, 0xffff5bb1), (s14, 0x895cd7be), (s11, 0x6b901122), (s12, 0xfd987193), (s13, 0xa679438e), (s14, 0x49b40821)] r2 = [(s21, 0xf61e2562), (s22, 0xc040b340), (s23, 0x265e5a51), (s24, 0xe9b6c7aa), (s21, 0xd62f105d), (s22, 0x2441453), (s23, 0xd8a1e681), (s24, 0xe7d3fbc8), (s21, 0x21e1cde6), (s22, 0xc33707d6), (s23, 0xf4d50d87), (s24, 0x455a14ed), (s21, 0xa9e3e905), (s22, 0xfcefa3f8), (s23, 0x676f02d9), (s24, 0x8d2a4c8a)] r3 = [(s31, 0xfffa3942), (s32, 0x8771f681), (s33, 0x6d9d6122), (s34, 0xfde5380c), (s31, 0xa4beea44), (s32, 0x4bdecfa9), (s33, 0xf6bb4b60), (s34, 0xbebfbc70), (s31, 0x289b7ec6), (s32, 0xeaa127fa), (s33, 0xd4ef3085), (s34, 0x4881d05), (s31, 0xd9d4d039), (s32, 0xe6db99e5), (s33, 0x1fa27cf8), (s34, 0xc4ac5665)] r4 = [(s41, 0xf4292244), (s42, 0x432aff97), (s43, 0xab9423a7), (s44, 0xfc93a039), (s41, 0x655b59c3), (s42, 0x8f0ccc92), (s43, 0xffeff47d), (s44, 0x85845dd1), (s41, 0x6fa87e4f), (s42, 0xfe2ce6e0), (s43, 0xa3014314), (s44, 0x4e0811a1), (s41, 0xf7537e82), (s42, 0xbd3af235), (s43, 0x2ad7d2bb), (s44, 0xeb86d391)] s11 = 7 s12 = 12 s13 = 17 s14 = 22 s21 = 5 s22 = 9 s23 = 14 s24 = 20 s31 = 4 s32 = 11 s33 = 16 s34 = 23 s41 = 6 s42 = 10 s43 = 15 s44 = 21 -- ===================== CONVERSION FUNCTIONS ======================== -- Turn the 4 32 bit words into a string representing the hex number they -- represent. abcd_to_string :: ABCD -> String abcd_to_string (ABCD (a,b,c,d)) = concat $ map display_32bits_as_hex [a,b,c,d] -- Split the 32 bit word up, swap the chunks over and convert the numbers -- to their hex equivalents. display_32bits_as_hex :: Word32 -> String display_32bits_as_hex w = swap_pairs cs where cs = map (\x -> getc $ (shiftR w (4*x)) .&. 15) [0..7] getc n = (['0'..'9'] ++ ['a'..'f']) !! (fromIntegral n) swap_pairs (x1:x2:xs) = x2:x1:swap_pairs xs swap_pairs _ = [] -- Convert to an integer, performing endianness magic as we go abcd_to_integer :: ABCD -> Integer abcd_to_integer (ABCD (a,b,c,d)) = rev_num a * 2^(96 :: Int) + rev_num b * 2^(64 :: Int) + rev_num c * 2^(32 :: Int) + rev_num d rev_num :: Word32 -> Integer rev_num i = toInteger j `mod` (2^(32 :: Int)) -- NHC's fault ~~~~~~~~~~~~~~~~~~~~~ where j = foldl (\so_far next -> shiftL so_far 8 + (shiftR i next .&. 255)) 0 [0,8,16,24] -- Used to convert a 64 byte string to 16 32bit words string_to_word32s :: String -> [Word32] string_to_word32s "" = [] string_to_word32s ss = this:string_to_word32s ss' where (s, ss') = splitAt 4 ss this = foldr (\c w -> shiftL w 8 + (fromIntegral.ord) c) 0 s -- Used to convert a list of 512 bools to 16 32bit words bools_to_word32s :: [Bool] -> [Word32] bools_to_word32s [] = [] bools_to_word32s bs = this:bools_to_word32s rest where (bs1, bs1') = splitAt 8 bs (bs2, bs2') = splitAt 8 bs1' (bs3, bs3') = splitAt 8 bs2' (bs4, rest) = splitAt 8 bs3' this = boolss_to_word32 [bs1, bs2, bs3, bs4] bools_to_word8 = foldl (\w b -> shiftL w 1 + if b then 1 else 0) 0 boolss_to_word32 = foldr (\w8 w -> shiftL w 8 + bools_to_word8 w8) 0 -- Convert the size into a list of characters used by the len_pad function -- for strings length_to_chars :: Int -> Word64 -> String length_to_chars 0 _ = [] length_to_chars p n = this:length_to_chars (p-1) (shiftR n 8) where this = chr $ fromIntegral $ n .&. 255